The Fractional Quantum Hall States of Dirac Electrons in Graphene

TL;DR

This paper explores how the relativistic energy dispersion of Dirac electrons in graphene influences fractional quantum Hall states across different Landau levels, revealing level-dependent energy gaps and polarization states.

Contribution

It provides a detailed analysis of fractional quantum Hall states in graphene, highlighting the impact of relativistic dispersion on energy gaps and valley polarization across Landau levels.

Findings

Energy gaps are largest at ν=1/m in the n=1 Landau level.

Valley-unpolarized states are favored at 2/3 filling in both n=0 and n=1 levels.

Energy gaps are suppressed in the n=1 level for certain states compared to n=0.

Abstract

We have investigated the fractional quantum Hall states for the Dirac electrons in a graphene layer in different Landau levels. The relativistic nature of the energy dispersion relation of the electrons in the graphene significantly modifies the inter-electron interactions. This results in a specific dependence of the ground state energy and the energy gaps for electrons on the Landau level index. For the valley-polarized states, i.e. at \nu =1/m, m being an odd integer, the energy gaps have the largest values in the n=1 Landau level. For the valley-unpolarized states, e.g., for the 2/3 state, the energy gaps are suppressed for the n=1 Landau level as compared to the n=0 level. For both the n=1 and n=0 Landau levels the ground state of the 2/3 system is fully valley-unpolarized.